Feedback control systems are widely used to maintain the output of a dynamic system at a desired value in spite of external disturbances that would displace it from the desired value. For example, a household space heating furnace, controlled by a thermostat, is an example of a feedback control system. The thermostat continuously measures the air temperature inside the house, and when the temperature falls below a desired minimum temperature the thermostat turns the furnace on. When the interior temperature reaches the desired minimum temperature, the thermostat turns the furnace off. The thermostat-furnace system maintains the household temperature at a substantially constant value in spite of external disturbances such as a drop in the outside temperature. Similar types of feedback controls are used in many applications.
A central component in a feedback control system is a controlled object, a machine or a process that can be defined as a “plant”, whose output variable is to be controlled. In the above example, the plant is the house, the output variable is the interior air temperature in the house and the disturbance is the flow of heat (dispersion) through the walls of the house. The plant is controlled by a control system. In the above example, the control system is the thermostat in combination with the furnace. The thermostat-furnace system uses a simple on-off feedback control system to maintain the temperature of the house. In many control environments, such as motor shaft position or motor speed control systems, simple on-off feedback control is insufficient. More advanced control systems rely on combinations of proportional feedback control, integral feedback control, and derivative feedback control. A feedback control based on a sum of proportional, plus integral, plus derivative feedback, is often referred as a PID control.
A PID control system is a linear control system that is based on a dynamic model of the plant. In classical control systems, a linear dynamic model is obtained in the form of dynamic equations, usually ordinary differential equations. The plant is assumed to be relatively linear, time invariant, and stable. However, many real-world plants are time varying, highly nonlinear, and unstable. For example, the dynamic model may contain parameters (e.g., masses, inductance, aerodynamics coefficients, etc.) which are either only approximately known or depend on a changing environment. If the parameter variation is small and the dynamic model is stable, then the PID controller may be satisfactory. However, if the parameter variation is large or if the dynamic model is unstable, then it is common to add adaptive or intelligent (AI) control functions to the PID control system.
AI control systems use an optimizer, typically a nonlinear optimizer, to program the operation of the PID controller and thereby improve the overall operation of the control system.
Classical advanced control theory is based on the assumption that near equilibrium points all controlled “plants” can be approximated as linear systems. Unfortunately, this assumption is rarely true in the real world. Most plants are highly nonlinear, and often do not have simple control algorithms. In order to meet these needs for a nonlinear control, systems have been developed that use soft computing concepts such as genetic algorithms (GA), fuzzy neural networks (FNN), fuzzy controllers and the like. By these techniques, the control system evolves or changes in time to adapt itself to changes that may occur in the controlled “plant” and/or in the operating environment.
A control system for controlling a plant based on soft computing is depicted in FIG. 1. Using a set of inputs, and a fitness function, the genetic algorithm works in a manner similar to an evolutional process to arrive at a solution which is, hopefully, optimal.
The genetic algorithm generates sets of “chromosomes” (that is, possible approaches) and then sorts the chromosomes by evaluating each approach using the fitness function. The fitness function determines where each approach ranks on a fitness scale. Chromosomes (approaches) which are more fit, are those which correspond to approaches that rate high on the fitness scale. Chromosomes which are less fit, are those which correspond to approaches that rate low on the fitness scale.
Chromosomes that are more fit are kept (survive) and chromosomes that are less fit are discarded (die). New chromosomes are created to replace the discarded chromosomes. The new chromosomes are created by crossing pieces of existing chromosomes and by introducing mutations.
The PID controller has a linear transfer function and thus is based upon a linearized equation of motion for the controlled “plant”. Prior art genetic algorithms used to program PID controllers typically use simple fitness and thus do not solve the problem of poor controllability typically seen in linearization models. As is the case with most optimizers, the success or failure of the optimization often ultimately depends on the selection of the performance (fitness) function.
Evaluating the motion characteristics of a nonlinear plant is often difficult, in part due to the lack of a general analysis method. Conventionally, when controlling a plant with nonlinear motion characteristics, it is common to find certain equilibrium points of the plant, and the motion characteristics of the plant are linearized in a vicinity near an equilibrium point. Control is then based on evaluating the pseudo (linearized) motion characteristics near the equilibrium point. This technique is scarcely, if at all, effective for plants described by models that are unstable or dissipative.
Computation of optimal control based on soft computing includes a GA as the first step of global search for an optimal approach on a fixed space of positive approaches. The GA searches for a set of control weights for the plant. First, the weight vector K={k1, . . . , kn} is used by a conventional proportional-integral-differential (PID) in the generation of a signal δ(K) which is applied to the plant. The entropy S(δ(K)) associated to the behavior of the plant on this signal is assumed as a fitness function to minimize. The GA is repeated several times at regular time intervals in order to produce a set of weight vectors. The vectors generated by the GA are then provided to a FNN, and the output of the FNN are provided to a fuzzy controller. The output of the fuzzy controller is a collection of gain schedules for the PID-controller that controls the plant. For soft computing systems based on the GA, there is very often no real control law in the classical control sense, but rather, control is based on a physical control law such as minimum entropy production.
This allows robust control because the GA, combined with feedback, guarantees robustness. However, robust control is not necessarily optimal control. The GA attempts to find a global optimum approach for a given approach space. Any random disturbance (m(t) in FIG. 1) of the plant can “kick” the GA into a different approach space.
It is desirable, however, to search for a global optimum in multiple approach spaces in order to find a “universal” optimum.
The application of new knowledge-based control algorithms in advanced intelligent control theory of complex dynamic systems (as in controlling objects) has brought the development of new processing methods, such as Computational Intelligence (CI). Traditional computing basic tools for CI is the GA, FNN, Fuzzy Sets theory, Evolution Programming, and Qualitative Probabilistic Reasoning, etc. Application of CI in the advanced control theory of complex system motion has brought two ways to research: 1) the study of stable non-equilibrium motion; and 2) an unstable non-equilibrium motion of complex dynamic systems.
In the first case (of stable non-equilibrium motion) the development and design of intelligent control algorithms can be described in the structure illustrated in FIG. 1.
The peculiarity of the given structure is the consideration of the control object in accordance with the fuzzy system theory as a “black box” or non-linear models of plants. The study and optimization of “input-output” relations is based on soft computing as GA, FNN and fuzzy control (FC) for the description of the changing law of a PID-controller parameters with a minimum entropy production and control error. At the small random initial states, uncontrollable external excitations or a small change of parameters or a structure of controlled objects (plants) guarantees a robust and stable control for fixed spaces of possible excitations and approaches.
In case of a global unstable dynamic control objective such an approach based on the presence of a robust and stable control does not guarantee success in principle. For this kind of unstable dynamic control objectives, the development of new intelligent robust algorithms based on the knowledge about a movement of essentially non-linear unstable non-holonomic dynamic systems is necessary.